Real-time feedrate scheduling for five-axis machining by simultaneously planning linear and angular trajectories

Feedrate scheduling for five-axis CNC machining is challenging due to the additional non-linear angular motion. Traditional real-time feedrate scheduling methods usually only concern the linear (i.e., tool position) motion, and synchronize the angular (i.e., tool orientation) motion with the linear motion by sharing the same curve parameter. The resultant angular motion will violate the angular constraints and be discontinuous at block junctions. This paper presents a real-time feedrate scheduling method for five-axis machining by simultaneously planning linear and angular trajectories (SLATP). The SLATP treats the angular motion equally with the linear motion, resulting in smooth linear and angular trajectories considering axial kinematic constraints in real time. The linear and angular boundary velocities are firstly determined by implicit circular blending on R3 and S2. Then, the linear and angular trajectories are separately planned with piecewise polynomial profiles. Finally, a bi-directional scanning method with time synchronization is proposed to make the velocity overall continuous. During each scanning, the linear and angular trajectories are time synchronized with an analytical algorithm. The synchronization algorithm is compatible with the traditional bi-directional scanning method and feasible for toolpaths consisting of multiple blocks. The SLATP strictly respects the linear and angular kinematic constraints in the workpiece coordinate system. It can also consider the axial kinematic constraints by mapping these constraints into the workpiece coordinate system. Simulations and experiments have demonstrated that the SLATP can plan smoother axial trajectories within about 140μs and achieve smaller contour errors compared with traditional real-time methods.